The modern era brings us the opportunities and challenges of big data, where both sample sizes and dimensions increase out of the capacity of classical statistical methods. Examples of the large scale datasets include: millions of spectra collected by astronomical surveys (e.g. LAMOST of [1]} and SDSS of [2]}); petabyte amounts of hyperspectral images recorded by airborne or satellite remote sensing [3]}; brain medical images through the functional magnetic resonance imaging [4]}, [5]}. A common characteristic of these datasets is that their observations can be viewed as functions over some continuous domain (e.g. temporal or spatial domain), and functional data analysis [6]} can serve as a designated toolbox. FDA treats functional observations as realizations of some stochastic process with low intrinsic dimension in an infinite dimensional Hilbert space. This means observations can be effectively approximated by splines, wavelets or linear combinations of a few functional principal components. In contrast to classical multivariate methods, FDA takes these features into consideration to achieve optimal convergence rates. Despite their demonstrated value in theory and application, the current FDA methods lack the scalability for modern large scale datasets [7]}.
